zzq@zzq-virtual-machine:~/y927/gpt-linuxroot-system-home-udisk$ sgdisk -p y927-original-gpt.img Caution: invalid backup GPT header, but valid main header; regenerating backup header from main header.
Warning! Main and backup partition tables differ! Use the 'c' and 'e' options on the recovery & transformation menu to examine the two tables.
Warning! One or more CRCs don't match. You should repair the disk! Main header: OK Backup header: ERROR Main partition table: OK Backup partition table: ERROR **************************************************************************** Caution: Found protective or hybrid MBR and corrupt GPT. Using GPT, but disk verification and recovery are STRONGLY recommended. **************************************************************************** Warning! Secondary partition table overlaps the last partition by 11333631 blocks! Try reducing the partition table size by 45334524 entries. (Use the 's' item on the experts' menu.) Disk y927-original-gpt.img: 30535680 sectors, 14.6 GiB Sector size (logical): 512 bytes Disk identifier (GUID): 98101B32-BBE2-4BF2-A06E-2BB33D000C20 Partition table holds up to 32 entries Main partition table begins at sector 2 and ends at sector 9 First usable sector is 34, last usable sector is 0 Partitions will be aligned on 2-sector boundaries Total free space is 0 sectors (0 bytes)
~ # busybox ls /sys/class/net/ lo wlan0 ~ # busybox ip link set wlan0 up ~ # busybox ip link show wlan0 2: wlan0: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc noqueue qlen 1000 link/ether 02:00:06:9a:cc:1b brd ff:ff:ff:ff:ff:ff
~ # evtest /dev/input/event3 Input driver version is 1.0.1 Input device ID: bus 0x18 vendor 0x416 product 0x23c7 version 0x1015 Input device name: "Goodix Capacitive TouchScreen" Supported events: Event type 0 (EV_SYN) Event type 1 (EV_KEY) Event code 330 (BTN_TOUCH) Event type 3 (EV_ABS) Event code 0 (ABS_X) Event code 1 (ABS_Y) Event code 24 (ABS_PRESSURE) Event code 47 (ABS_MT_SLOT) Event code 48 (ABS_MT_TOUCH_MAJOR) Event code 53 (ABS_MT_POSITION_X) Event code 54 (ABS_MT_POSITION_Y) ... Testing ... (interrupt to exit)
按下手指时输出形如：
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Event: time 12.345, type 3 (EV_ABS), code 53 (ABS_MT_POSITION_X), value 360 Event: time 12.345, type 3 (EV_ABS), code 54 (ABS_MT_POSITION_Y), value 640 Event: time 12.345, type 1 (EV_KEY), code 330 (BTN_TOUCH), value 1 Event: time 12.345, -------------- SYN_REPORT ------------
Device Boot StartCHS EndCHS StartLBA EndLBA Sectors Size Id Type /dev/mmcblk0p1 0,0,1 1023,255,63 1 4294967295 4294967295 2047G ee EFI GPT Disk /dev/mmcblk1: 7619M, 7989100544 bytes, 15603712 sectors 3504 cylinders, 73 heads, 61 sectors/track Units: cylinders of 4453 * 512 = 2279936 bytes
Device Boot StartCHS EndCHS StartLBA EndLBA Sectors Size Id Type /dev/mmcblk1p1 0,130,3 971,72,61 8192 15603711 15595520 7615M b Win95 FAT32 Disk /dev/mmcblk0boot0: 4096K, 4194304 bytes, 8192 sectors 128 cylinders, 4 heads, 16 sectors/track Units: cylinders of 64 * 512 = 32768 bytes
Disk /dev/mmcblk0boot0 doesn't contain a valid partition table Disk /dev/mmcblk0boot1: 4096K, 4194304 bytes, 8192 sectors 128 cylinders, 4 heads, 16 sectors/track Units: cylinders of 64 * 512 = 32768 bytes Disk /dev/mmcblk0boot1 doesn't contain a valid partition table
第3阶段：真正的DRM显示（HX8394A 面板驱动移植）
目标
在lk1st的移植过程中，已经用lmdpdg.py工具反编译生成了完整的 Linux DRM panel 驱动，驱动源码在 ~/y927/linux-mdss-dsi-panel-driver-generator/workdir/dtb/plat_ce-var_1-sub_0/hx8394a_720p_video 这一阶段将这一驱动移植到主线 Linux 内核中。
alias edl='uvx --from git+https://github.com/bkerler/edl.git edl --loader=~/y927/prog_emmc_firehose_8916.mbn'
edl r modem ~/y927/backup/modem.img # IMEI 主存储 ⚠️ 必须备份 edl r fsg ~/y927/backup/fsg.img # IMEI 备份 ⚠️ 必须备份
# 以下分区线刷包中都有，备份只是节省恢复时间 edl r sbl1 ~/y927/backup/sbl1.img edl r tz ~/y927/backup/tz.img edl r hyp ~/y927/backup/hyp.img edl r aboot ~/y927/backup/aboot.img edl r rpm ~/y927/backup/rpm.img
cd ~/y927 mkdir wget https://releases.linaro.org/96boards/dragonboard410c/linaro/rescue/17.09/dragonboard410c_bootloader_emmc_android-88.zip unzip dragonboard410c_bootloader_emmc_android-88.zip tz.mbn rm dragonboard410c_bootloader_emmc_android-88.zip
编译 qhypstub
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cd ~/y927 git clone https://github.com/msm8916-mainline/qhypstub.git cd qhypstub git clone https://github.com/msm8916-mainline/qtestsign.git make CROSS_COMPILE=aarch64-linux-gnu-
alias edl="uvx --from git+https://github.com/bkerler/edl.git edl --loader=$HOME/y927/prog_emmc_firehose_8916.mbn"
# 刷入三个分区（sbl1 保留原厂） edl w tz $HOME/y927/tz.mbn edl w hyp $HOME/y927/qhypstub/qhypstub-test-signed.mbn edl w aboot $HOME/y927/lk2nd/build-lk1st-msm8916/emmc_appsboot-test-signed.mbn
voidrenderTriangle(const Triangle& tri, FrameBuffer& frameBuffer, DepthBuffer& depthBuffer){ for (int x = 0; x < frameBuffer.width; x++) { for (int y = 0; y < frameBuffer.height; y++) { float z = inside(tri, x + 0.5f, y + 0.5f); if (z < depthBuffer.getDepth(x, y)) { frameBuffer.setColor(x, y, tri.color); depthBuffer.setDepth(x, y, z); } } } }
use std::sync::{Arc, Mutex}; use vm_device::bus::{PioAddress, PioAddressOffset, PioRange}; use vm_device::device_manager::{IoManager, PioManager}; use vm_device::MutDevicePio;
use std::fs::File; use linux_loader::loader::bzimage::BzImage; // 也可换成 elf::Elf / pe::PE use linux_loader::loader::{KernelLoader, load_cmdline, Cmdline}; use vm_memory::{GuestAddress, GuestMemoryMmap};
声明：以下是概念性骨架，目的在于展示 API 拼装方式与控制流，省略了真正启动 Linux 所需的若干细节（boot params zero-page、CPUID/MSR、IDT、页表、APIC/GIC、ACPI/FDT、MPTABLE 等架构相关初始化）。要跑起一个真实 Linux Guest，请直接参考 vmm-reference。
use kvm_bindings::{kvm_userspace_memory_region, KVM_MEM_LOG_DIRTY_PAGES}; use kvm_ioctls::{Kvm, VcpuExit}; use linux_loader::loader::{elf::Elf, KernelLoader}; use std::fs::File; use vm_memory::{Address, GuestAddress, GuestMemoryMmap};
from math import pi, sqrt from functools import reduce
defC(a: float, b: float, m: int)-> float: a, b = (a, b) if a > b else (b, a) # 确保a是长半轴 c = sqrt(a**2 - b**2) e = c / a return2 * pi * a * (1-sum( map( lambda n: ((e**(2*n)) / (2*n - 1)) * (reduce( lambda x, y: x * y, map( lambda k: (2*k - 1) / (2*k), range(1, n+1), ), )) ** 2, range(1, m+1), ), ))
# 逐步收敛到一个确定的值 15.86543958929059 for i inrange(1, 100): print(C(3, 2, i))
classSolution { public: intnumberOfArrays(vector<int>& differences, int lower, int upper){ int a_min = 0, a_max = 0; // 还原整个数组a的过程中记录a的最小和最大值 int cur = 0; // 选定一个常数标记a[0]起始值 for (int diff: differences) { cur += diff;
defprintAddTable(): print('|+|', end="") for i inrange(modulus): print(f'{i}|', end="") print()
print("|-|", end="") for i inrange(modulus): print(f'-|', end="") print()
for i inrange(modulus): print(f'|{i}|', end="") for j inrange(modulus): print(add(i, j), end="|") print()
printAddTable()
print('\n\n乘法运算表')
defprintMulTable(): print('|*|', end="") for i inrange(modulus): print(f'{i}|', end="") print()
print("|-|", end="") for i inrange(modulus): print(f'-|', end="") print()
for i inrange(modulus): print(f'|{i}|', end="") for j inrange(modulus): print(mul(i, j), end="|") print()
printMulTable()
print('\n\n方程验算表')
defprintEquationTable(): solved = [] print('|(x,y)|y^2+x=x^3|等号成立性|') print("|-|-|-|") for y inrange(modulus): for x inrange(modulus): left = add(mul(y, y), x) right = mul(mul(x, x), x) eq = left == right if eq: solved.append((x, y)) print(f'|({x},{y})|{y}^2+{x}={x}^3|{"成立"if eq else"不成立"}|') print(f'\n方程一共有{len(solved)}个解，分别为 {solved}')
defs() -> int: solved = 0 for y inrange(p): for x inrange(p): left = add(mul(y, y), x) right = mul(mul(x, x), x) eq = left == right if eq: solved += 1 return solved return s()
defprime_list(n: int) -> list[int]: primes = [] for i inrange(2, n + 1): for j inrange(2, i): if i % j == 0: break else: primes.append(i) return primes
defmain(): primes = prime_list(23) print('|p|s(p)|') print('|-|-|') for p in primes: print(f'|{p}|{s(p)}|')
main()
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10.5 自守形式的世界
下面这个函数有一个非常有意思的性质：
ϕ(z)=e2πiz∏_k=1∞(1−e8kπiz)2(1−e16kπiz)2
ϕ(z)是自守形式的一种。
设a,b,c,d是整数且满足ad−bc=1, c 是 32 的倍数，根据z=u+iv，可以得到以下等式成立：
s = set() for n inrange(2,1+8): for m inrange(1,n): # m,n 互质 if gcd(m, n) == 1: x = 12 * (log(n,2) - log(m, 2)) print(f'|{m}|{n}|{round(x,2)}|{round(x)}|') s.add(round(x))
透视投影摄像机的视线范围由一个平头四棱台体所确定，使得内部的物体可以呈现近大远小的效果。 我们可以想象以下直接通过“挤压”将平头四棱台挤压为一个长方体，变换前后 n 平面上的点不变，n~f 平面上的点将被压缩，越接近 f 平面，点被压缩的越厉害，所以当变换到长方体后相同的三维几何体离 f 平面越近投影后的图像就越小，故能够呈现出近大远小的效果。这也是一种空间变换，但它在三维空间中属于一种非线性变换，如果我们希望使用矩阵描述，则需要借助齐次坐标将其放置在四维空间中完成这个变换。
当我们从透视投影的平头四棱台空间压缩变换到平行投影的长方体后，对于内部的任意一点(x,y,z)坐标，变换后对应的坐标为(x′,y′,z′)，显然是可以得到z越远的点，(x′,y′)坐标被压缩的越厉害，关系式可在上述推导中体现。但是内部任意一个点的 z 坐标在变换前后就没有那么直观，我们可以进一步做一系列推导。
]]><p>文件系统的目的是为了组织和存放数据。文件系统通常是为了用户之间和应用程序之间共享数据使用，同时还能够实现持久话存储，以便于数据在重启之后依旧可用。</p>
<p>xv6文件系统提供了类Unix的文件，目录和路径名称，并且存储它的数据在virtio磁盘以持久话数据。文件系统需[论文翻译] Review of FAT data structure of FAT32 file systemhttps://zhangzqs.cn/posts/949/2023-01-11T06:53:47.000Z2023-01-11T06:53:47.000Z 原始 Paper
M. S. Kwon, S. H. Bae, S. S. Jung, D. Y. Seo, and C. K. Kim, “KFAT: Log-based Transactional FAT File system for Embedded Mobile Systems”, In Proceedings of 2005 US-Korea Conference, ZCTS-142, 2005
Liang Alei, Liu Kejia, Li Xiaoyong , “FATTY :A reliable FAT File System”, Proceedings of the 10th Euromicro Conference on Digital System Design Architectures, Methods and Tools, Pages: 390-395, 2007.
FATTY: 一个可靠的FAT文件系统
Standards - Ecma-107
Standards - ISO 9293:1987
Standards - ISO/IEC 9293:1994
Michael D. Dahlin, “The Impact of Trends in Technology on File System Design“ University of California, Berkeley, January 23,
usecase 使用分页 as usePage User --> usePage usecase 切换当前页面 as switchPage usecase 增加新页面 as addPage usecase 删除非当前页 as deletePage usePage <-- switchPage: <<extends>> usePage <-- addPage: <<extends>> usePage <-- deletePage: <<extends>> @enduml
创建图元
用户可以在白板上创建各式各样的图形元素，至少需要包含直线、矩形、椭圆、文本框、自由路径的绘制等等。
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left to right direction usecase 创建图形元素 as createComponent User --> createComponent usecase 创建直线 as createLine usecase 创建矩形 as createRect usecase 创建椭圆 as createOval usecase 创建文本框 as createText usecase 创建自由路径 as createPath createComponent <-- createLine: <<extends>> createComponent <-- createRect: <<extends>> createComponent <-- createOval: <<extends>> createComponent <-- createText: <<extends>> createComponent <-- createPath: <<extends>>
操作历史
用户能够操作历史线，实现回滚与重做功能。
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left to right direction usecase 操作历史 as controlHistory User --> controlHistory usecase 回滚 as undo usecase 重做 as redo controlHistory <-- undo: <<extends>> controlHistory <-- redo: <<extends>>
left to right direction usecase 操作工程文件 as project User --> project usecase 保存工程 as save usecase 另存为工程 as saveAs usecase 打开工程 as open project <-- save: <<extends>> project <-- saveAs: <<extends>> project <-- open: <<extends>>
actor 主持人 as Owner Owner --|> User usecase 创建进入白板房间 as createAndEnter usecase 复制房间id as copyId usecase 修改白板模式 as modifyMode Owner --> createAndEnter Owner --> copyId Owner --> modifyMode
actor 普通成员 as Member Member --|> User usecase 加入白板房间 as enter usecase 查看同步画板 as look Member --> enter Member --> look
@startuml D Member -> Owner: 发起请求 ...等待响应... alt [未收到响应数据] Member -> Member: 房间号不存在 else [收到全量数据] Owner -> Member: 全量数据 loop Owner数据存在更新 Owner -> Member: 增量补丁 Member -> Member: 变更本地数据 end end @enduml
// 求解大整数幂模m^n mod q intsolve(int m, int n, int q) { // 分解到不可再分 // 如果n==1那么直接输出结果 if (n == 1) return m % q; // 二分法分解 // 计算s=m^(n/2) mod q int s = solve(m, n / 2, q); // 预计算r=(m^(n/2) * m^(n/2)) % q int r = s * s % q; // 若为奇数次幂则为(m^(n/2) * m^(n/2) * m) % q if (n % 2) return (r * (m % q)) % q; // 偶数次幂则为(m^(n/2) * m^(n/2)) % q return s * s % q; }
